Electrical servo system



May 21, 1957 T. E. WOODRUFF ELECTRICAL sERvo sYsTEu 2 Sheets-Sheet 1Original Filegi July 29, 1949 2 Sheets-Sheet 2 T. E. WOODRU FF May 21,1957 ELECTRICAL SERVO SYSTEM Original Filed July 29, 1949 M ZKM www E y,J 9 M n United States Patent O ELECTRICAL SERVO SYSTEM Thomas E.Woodrulf, Los Angeles, Calif., assiguor to Hughes Aircraft Company,Culver City, Calif., a corporation of Delaware Original application July29, 1949, Serial No. 107,558, now Patent No. 2,701,328, dated February1, 1955. Divided and this application September 14, 1954, SerialNo.455,834

6 Claims. (Cl. S18-18) The present invention relates to electrical servosystems and more particularly to an improved control circuit for closedloop automatic control systems. This application is a division of UnitedStates patent application, Serial No. 107,558, led July 29, 1949, forElectrical Servo System, by Thomas E. Woodrut, now Patent No. 2,701,328.

Stated in somewhat general terms, an electrical servo system includes asystem unbalance detector for obtaining an error signal corresponding tothe displacement of a load device from a normal or desired position, areversible servomotor mechanically coupled to the load device to correctits displacement, means for deriving control signals from the errorsignal, and means for controlling the energization of the servomotor inaccordance with the control signals to move the load device toward thedesired position. The servo loop or closed-cycle control system thusformed drives the load device toward the desired position whenever adisplacement develops, and tends to maintain the error or displacementat or near zero value.

While the many servo systems thus far developed are adequate for mostpurposes, certain precise equipments utilizing servo systems demand anaccuracy and speed of response not attainable with conventional servosystems. ln proportional control systems, for example, the energizationof the servomotor is increased with the load displacement, the torqueand speed developed by the servomotor are correspondingly dependent uponthis displacement, and the response speed or time taken to overcome theload displacement is correspondingly much greater than is ideallynecessary.

lt is accordingly the principal object of the present invention toprovide an electrical servo system having improved performancecharacteristics.

Another object of the invention is to provide a servo system in whichdisplacements are overcome by utilizing to full capacity theacceleration and deceleration capabilities of the systems servomotor.

An additional object of the invention is to provide a high-speed servosystem in which load displacements are overcome by rst fully energizingthe systems servomotor in a restoring direction, anticipating the pointat which reversal of the energization of the servomotor would restorethe load of its normal position, and reversing the energization of theservomotor substantially at the anticipated point.

Still another object of the invention is to provide a servo systemwherein the load, when displaced, is driven toward the point of zerodisplacement and zero velocity by fully energizing the servomotor, theenergization of the servomotor being reversed immediately after the loadhas reached a point whereat reversal of its energization would returnthe load to the point of zero velocity and zero displacement, the pointof reversal of the servomotor being anticipated from the magnitude ofthe displacement and the time rate of change of the `displacement.

These and other objects and advantages of the present invention willbecome apparent trom consideration of the ICC following description,taken with reference to the accompanying drawings in which:

Figure l is a block diagram of an electrical servo system embodying thepresent invention;

Fig. 2 is a schematic diagram of one form of control signal circuitapplicable tothe system of Fig. l and is here shown to illustrate theunderlying concept of the invention;

Fig. 3 is a circuit diagram of one form of motor control unit which maybe employed in the system of Fig. l;

Fig. 4 is a graph illustrating system load movements effected by thecontrol signal circuit of Fig. 2;

Fig. 5 is a schematic diagram of the control signal circuit, accordingto the invention, which is utilized in the system of Fig. l;

Fig. 6 is a graph illustrating system load movements effected by thecontrol signal circuit of the invention as shown in Fig. 5; and

Fig. 7 is a circuit diagram of one electrical circuit which may beemployed in the control circuits of Figs. 2 and 6.

While the principles involved in the present invention may be applied tothe design of many forms of automatic control systems, the embodimentherein described by way of example contemplates servo systems whichinclude a system load subject to angular displacement and a. servomotoryielding rotational drive for correction of the displacement. lndescribing the invention, load displacements and certain factorsassociated therewith are referred to as either positive or negative inaccordance with the sense or direction in which they occur or act. Thus,assuming a torque acting in a given direction to be positive, therotations, velocities, and accelerations are positive when acting ortaking place in that direction and negative when in the oppositedirection.

Similarly, displacements are termed positive or negative when they arein the direction of positive or negative rotation, respectively, asmeasured from some normal position. It is also to be understood that theterms acceleration and deceleration as herein utilized, signify actionsin which the velocity or time rate of change of the displacementincreases or decreases, respectively, in magnitude. The symbolsdesignating various signals later referred to also designate the angulardisplacements and time-functions thereof to which the signalscorrespond. lt is to be further understood that while suitableamplification and proportionality factors are, of course, necessary inactual design of the equipment, they are here omitted for purposes ofsimplification.

The basic principle of the present invention is the utilization of fullservomotor drive at all times during all portions of adisplacement-correction cycle, that is, both in accelerating anddecelerating the load toward the end conditions of essentially zerovelocity and zero displacement` For example, assuming an instance inwhich the system load experiences a displacement and is at rest at themoment that corrective action is initiated, an ideal cycle would involvefirst accelerating the system load toward zero displacement at fullcapability of the servomotor, anticipating the point at which fullenergization of the the servomotor in the reverse direction would returnthe load to zero displacement and zero velocity, and braking ordecelerating the system load at maximum capability of the servomotorwhen the anticipated point is reached to simultaneously return the loadto zero displacement and zero velocity. This ideal cycle achieves thefastest possible correction of system load displacement, and thepractical embodiments to be described closely approach such action.

Referring first to the general organization of the novel servo system asillustrated in block diagram form in Figure 1, the system load thereshown at 9 is positionable by a reversible servomotor 11 through gearingsche-` matically represented by dotted line 13. System load 9 includesmeans for developing an error or displacement signal 9 at an associatedoutput lead 15, the error signal having a characteristic which varies inaccordance with the instantaneous angular displacement 0 of system load9 from a desired position. System load 9 may, for example, be anelectro-optical apparatus including a sighting structure and means forproviding an error signal 0 corresponding to the deviation between thesighting structures pointing direction and the true line of sight to abright body in the field of view.

Error signal 9 is applied to the input circuit of a derivation orcontrol-signal circuit 17 which, in the specific embodiment to bedescribed hereinafter, develops signals having instantaneous valuesproportional to a first term involving the displacement 0 and to asecond term involving displacement rate or velocity 9', and summates thetwo signals to provide a control signal which at any instant is eitherpositive, negative, or zero depending upon the sense and relativemagnitudes of the two terms. The control signal output of derivationcircuit 17 is applied to a motor control unit 19, adapted to energizeservomotor l1 at full operating voltage at all times and, further, tocontrol the direction ol motor torque in accordance with the polarity ofthe control signal, effecting return of the load device toward zerodisplacement in a manner detailed hereinafter.

In order to further illustrate the underlying concept ot' the invention,it will first be assumed that control signal circuit 17 is arranged toprovide a control signal corresponding to the summation of a velocityterm l'i' and a displacement term Zll. In these expressions, arepresents the load displacement, which is either positive or negative,is a variable representing the time rate of change of the displacement 0and may be either positive or negative depending upon the direction ofrotation, it?! represents the absolute magnitude of the variablevelocity, and lat represents the absolute magnitude of the accelerationor deceleration of servomotor 11, which will be assumed to besubstantially constant over the range of load displacement. The termleila' is thus equal to 02 with sign corresponding to the sense ordirection of the velocity, while the term Zli similarly takes on thesign corresponding to the sense or direction of the displacement.

Referring now to Fig. 2, there is shown one form of control signalcircuit which may be employed to mechanize the illustrative conceptoutlined above. As shown in Fig. 2, error signal 0 is applied over lead15 to a diti'erentiator 21, which provides at an associated output lead23 a velocity signal o' proportional to the first timederivative ortime-rate of change of displacement 0. The velocity signal 0' is thenapplied to a squaring circuit 25 which produces an output signal lo'l,so expressed to indicate that its polarity is dependent upon the senseof velocity signal 0' rather than continuously positive as in truemathematical squaring.

Displacement signal 0 is also applied to an amplifier 27 which providesat an associated output lead 29 an output signal proportional to Zll.The factor ll S here set in as a fixed multiplier, since as previouslynoted, the acceleration and deceleration of the servomotor aresubstantially constant in magnitude over the normal operating range ofthe servomotor. The polarity of the signal Zll is thus dependent onlyupon the sense or direction of displacement 0.

Signal [t is applied over lead 31 to one input termina' 33 of asummation circuit which comprises two serially connected resistors 35and 37, while signal 2ll6 is applied over lead 29 to a second inputterminal 39 of the summation circuit. The resultant control signaldeveloped by the derivation circuit is in this instance proportional tothe sum of velocity term Ie'lo' and displacement termZi l0, and isapplied over lead 41 to the motor oontrol unit I9 shown in Figure l.

Motor control unit 19 may be designed to utilize fast tit) acting relayswitches in a circuit which functions to apply full operating voltage toservomotor 11, and further functions to cause the servomotor torque tobe developed in a positive or forward direction for negativecontrolsignals, and in a negative or reverse direction for positivecontrol-signals. servomotor 11 may be a D.C. motor, for example, andmotor control unit 19 may be arranged to reverse its armature or fieldconnections substantially at the instant of reversal of control signalpolarity. A suitable circuit which functions in such manner is shown inFigure 3, in which a relay amplifier 43, to which the control signalsare applied over lead 41, selectively energizes either of two relaycoils 45 and 47 to contro-l the position of linked switch arms 49 and 51in accordance with the control signal polarity and thereby' control thedirection of energzation of the servomotor. lt will be recognized, ofcourse, that numerous other electronic circuits may be utilized toprovide equivalent operation.

The operation of the servo system including the illustrative controlcircuit described hereinabove may be conveniently explained withreference to the graph shown in Figure 4, in which the time rate ofchange or velocity of the load displacement is plotted against systemload displacement. The curves 53 and S5 in Fig. 4 define the angulardisplacement and velocity conditions for which the control signal iszero, as expressed by the equation Points in the area lying abovezero-signal curves 53 and S5 therefore represent the conditions ofangular displacement and velocity for which the control signal ispositive, and similarly, the conditions resulting in a control signal ofnegative polarity are represented by points lying below the said curves.The further significance of curves 53 and 55 lies in the fact that theydelineate the precise conditions of displacement i9 and the displacementrate 0' at which deceleration of the servomotor at full capacity wouldcarry the system load to zero velocity at zero displacement.

In order to set forth more specifically the operation of theillustrative control circuit of Fig. 2, assume that the system load hasan initial negative displacement accompanied by a negative velocity asat the point A in Fig. 4 graph. It will be recognized that thecorresponding instantaneous value of the control signal produced by thecontrol signal circuit of Fig. 2 is negative. Accordingly, servomotor 11is energized at full applied voltage to exert its torque in a forward orpositive direction. decelerating the system load until zero velocity isreached, as indicated by tracing the lower portion ofpositiveacceleration curve 57 in a clockwise direction to the point B.Still under the influence of forwardly directed torque, the system loadthen accelerates toward zero displacement, the displacement and velocityconditions following along curve 57 and at some instant reaching valueswhich satisfy the zero control-signal curve 53, as indicated by theintersection point C.

Assuming the control signal to become positive and the driving torque tobecome negative at the very instant that the system load reaches thedisplacement and velocity conditions of point C, the forward or positivevelocity would then decrease under deceleration ll, the displacement andvelocity following along curve 53 in the indicated clockwise directionuntil zero velocity at zero displacement would be reached simultaneouslyat the point O. ln actual practice, however, the decelerating torquedoes not come into play at the very instant when the system loadconditions reach the zero controlsignal curve, but rather at a laterinstant, as at the intersection of the acceleration curve S7 and acontrol curve 59 which intersection is designated point D in Fig. 4.This delay between point C and point D is due to inherent time-lagsn the'system components such as the delay in the opening of the relays in themotor control unit. The

ensuing conditions of the system load follow along anegative-acceleration curve 61 in the indicated clockwise direction,again past the zero control-signal curve 55 to an intersection point Elying on a control curve 63, at which time the energization of theservomotor is again reversed. This action is continuous and causes thesystem load to quickly reach a final condition in which it oscillatesabout the point of zero displacement, as indicated by the closed loopconsisting of curves 65 and 67.

The oscillation or vibration produced at the load by the described servosystem is actually relatively fast and small in amplitude, for Figure 4represents to an enlarged scale the system behavior in the immediatevicinity of zero velocity and zero displacement. ln a typical instance,for example, in which the system includes a 28 volt, 1,52 horsepowerservomotor having an acceleration characteristic of 5,000 radians persecond per second as measured at the motor shaft, and in which theservomotor is coupled to the system load through 360 to l reductiongearing, the total or effective time-lag in the system is of the orderof 4 milliseconds. The frequency of the resultant stable oscillation isin this instance approximately 50 cycles per second, and its amplitudeas measured at the system load is of the order of one minute of angle.

It will be recognized that the configurations of the several curvesfollowed by the system load as above described are plotted from theappropriate equations of angular motion. Por example, curve 57 of theFigure 4 graph represents the particular positive-acceleration curveupon which the assumed initial point A falls, and is delined by theequation where is a fixed positive acceleration, flA and d, are,respectively, the system load displacement and velocity represented bythe point A, is the displacement at any point along the curve, and s' isthe corresponding velocity at that point. In terms of the displacement9B of point B at which the velocity becomes zero upon this curve, theequation may be rewritten as -D=2(09D) where has a negative value. Heretoo there is a family of such curves in which the appropriate curve mustagain be traced clockwise, in an increasing negative velocity direction,to trace successive conditions.

The positions and configurations of control curves 59 and 63 which areutilized to graphically find the points at which reversals of drivingtorque take place, may be determined by use of the formula Ag T in whichT is the effective delay time characteristic of the servo system, is theacceleration or deceleration, and A6 is the resultant change in velocitytaking place between the instant at which the control-signal becomeszero and the instant at which torque reversal actually takes place.Referring to positive-acceleration curve 57, for example, the diierencein velocities represented by points C and D thereon is equal to theproduct of the acceleration and delay time T. Since the acceleration anddelay time have lixed values, the velocity change is of constantmagnitude, in going between zero control-signal curve 53 or 55 andcontrol curve 59 or 63 along any acceleration curve.

Accordingly, control curves 59 and 63 thus may be readily plottedgraphically.

Although the control circuit shown in Fig. 2 has been found to be anexceptionally high speed device, the timedelay characteristic of a motorcontrol unit of the type shown in Fig. 3 is sufficiently large toproduce load oscillation which, though relatively small, is neverthelessundesirable for some servo applications. The novel controlsignal circuitof this invention, which is described hereinbelow, almost completelyovercomes this limitation by anticipating the point at which servomotorenergization should be reversed.

Referring now to Fig. 5, there is shown a control signal circuit,according to the invention, hich is arranged to produce a modifiedcontrol signal which reduces the ad verse effect of delay time inherentin the system components and approaches more closely the theoreticallyperf ect operation in which the system load is returned to zerodisplacement along the deceleration curve 53 as previously mentionedwith reference to Figure 4. As shown in Fig. 5, the control signalcircuit of the invention is similar to that shown in Fig. 2, with theexception that squaring circuit 2S of Fig. 2 is replaced by an amplifier7l, and the gains of amplifiers 71 and 27 are so adjusted that theiroutput signals are proportional to K0' and 0, respectively, where K is aconstant having an optimum value as later described. Accordingly, theresultant control signal from the summation network may be representedby the expression K-l- 9.

With reference now to Fig. 6, there is shown an operational diagram orgraph of the control circuit of Fig. 5 plotted to the same scale as thegraph of Fig. 4, and for the same acceleration constant and inherentdelay time. Deceleration curves S3 and 55 of Figure 4, defined by theexpression lfll-i-2l9l9, are here again shown for reference purposes. Aline 73 is shown as also intersecting the point ot' zero velocity andzero acceleration and defined by the equation IGH-0:() This line is thezero control-signal curve for the control circuit of the invention,while lines 7S and 77 are controlcurves representing the loci of pointsat which torque reversals actually take place, corresponding tocontrolcurves 59 and 63 in Figure 4.

ln operation, assume that the load is initially at point A as previouslydescribed for Fig. 4. Accordingly, the load decelerates along curve S7to the point B at which the velocity is zero, then accelerates to thepoint F at which zero control-signal line 73 is reached. The motortorque is actually reversed at a time later by the amount T, atdisplacement and velocity conditions indicated by the intersection atpoint G of acceleration curve 57 and control line 75. The continuingaction drives the system load to the condition of stable oscillationindicated by the closed loop 79. 8l, in this instance of considerablysmaller amplitude than the amplitude of the oscillation loop shown inFig. 4.

lt will be recognized that the amplitude of the load oscillation loop isdependent upon the slope of controlsignal line 73, becomes smaller asthe slope is made less by increasing K. An optimum value of K may inpractice be obtained by increasing the gain of amplifier 7l relative toamplifier 27 to a point where oscillation loop 79, 81 is suitably smallwithout severe reduction of the restoring torque. Usually this value 0iK is selected in view of the time-delay characteristic of the motorcontrol unit and is such that control curves 75 and 77 are almosttangent to curves 53 and 55.

Referring now to Fig. 7, there is shown a circuit diagram of adifferentiating circuit which may be utilized in the control circuit ofthe present invention, as shown in Fig. 5. It is to be understood, ofcourse, that this circuit is merely illustrative of one suitable form ofdifferentiator, and that other circuits may be used without departingfrom the spirit and scope of the present invention.

The differentiating circuit is substantially the same as that shown inFig. 4-14 on page 73 of vol. 2l of the M. I. T. Radiation LaboratorySeries entitled Electronic instruments," and published in 1948 by theMcGraw-Hill Book Company. in this circuit, inductor 101 and resistor 102form the differentiating elements, the output voltage, which appears onthe plate 103 of tube 104, being proportional to the first derivativewith respect to time of the input voltage which is applied to grid 105of tube 104.

It is apparent that many embodiments employing the principles of thepresent invention may be devised, utilizing conventional components andcircuitry giving end results which are quivalent to those achieved inthe embodiment above described. For example, the displacement ordeviation may be obtained in the form of an A.-C. signal having a phasecharacteristic related to the deviation 0. This signal may be suitablyamplified, then converted to a D.-C. signal 6 by a phase comparator.Differentiation may be accomplished by use of an RC circuit, andamplifiers, wherever necessary, may be of either D.-C. or A.C. signaltype suitably designed for the purpose. Similarly, many conventionaltypes of servomotor and reversing controls therefore are available, andmay be utilized in practice of the present invention. Thus, many changesand many widely different embodiments of the present invention could bemade without departing from its true scope. It is therefore intendedthat all matter contained in the preceding description or shown in theaccompanying drawings shall be interpreted as illustrativc and not in alimiting sense.

l claim as my invention:

l. A servo system for returning a displaced load to a predeterminedposition, said system comprising: a reversible motor for driving theload; an actuable motor control unit for continuously fully energizingsaid motor in a .selected direction to return the load to thepredeterminel position; displacement detection means responsive to thcdisplacement of the load for continuously producing a first electricalsignal corresponding to the load displacement; second means including afirst amplitier circuit coupled to said displacement detection means undresponsive to said first signal for continuously producing n secondelectrical signal whose magnitude and polarity are represented by the`term H where represents the loud displacement; third means coupled tosaid displacement detection means `and responsive to said first signalfor continuously producing a third electrical signal whose magnitude undpolarity `are represented by the term K6'. where a' represents the timerate of change of the load displacement und K represents aproportionality constant which is a function of the delay time of themotor control unit, said third means including a differentiating;cir-:nit coupled to said first means and responsive to said first signalfor producing a velocity signal correspending to the term fi, and asecond amplifier circuit connected to said differentiating circuit andresponsive to said velocity sign-ul for producing said third signal;:intl means coupled to said selectively actuable motor control unit,coupled to said second and third means :md responsive to said second andthird signals for selectively reversing the direction of cnergization ofsaid motor in accordance with reversals ofthe algebraic sense of thesummation of said second and third signals.

l. A\ servo st, i n:n for rapidly returning a displaced load to n pointofV` :cro displacement and zero velocity, said system comprising: areversible motor for driving the load, said motor being continuouslyfully energizable in a selected direction and having a substantiallyconstunt acceleration and deceleration characteristic over thc range ofloud displacement; a selectively actuablc motor control unit forcontinuously fully energizing said motor in either direction: and acontrol circuit for selectively actuating said selectively actuablemeans to fully energize said motor to drive said load toward a pointwhereat full energizaition of the motor in the opposite direction wouldreturn the load to the point of zero displacement and zero velocity,said control signal circuit including first means having an amplifierfor generating a first electrical signal represented by the term 6,where 0 represents the instantaneous load displacement; second meansincluding a. differentiator and an amplifier circuit connected incascade, said second means being responsive to the displacement of theload for continuously generating a second electrical signal proportionalto the term s', where s' represents the time rate of change of the loaddisplacement; summation means for combining said first and secondsignals to produce an output signal having a polarity corresponding tothe algebraic sense of the summation of said first and second signals;and means for applying said output signal to said selectively tactuablemotor control unit for reversing the energization of said motor inresponse to a change of polarity of said output signal.

3. A system for returning a displaced load toward a predeterminedposition, said system comprising: a reversible motor for driving theload, said motor being acceleratable and deceleratable at asubstantially constant rate over the range of load displacement; aselectively uctuable motor control unit for continuously fullyencrgizing said motor in either direction to return the load toward thepredetermined position; and control means continuously responsive to thedisplacement of the load (it) and to the time rate of change of thedisplacement (9') for selectively actuating said selectively actuablemeans, said control means including a difierentiator circuit fordeveloping a first electrical signal whose magnitude and polaritycorrespond to the term a first amplier coupled to said differentiatorcircuit and responsive to said first electrical signal for producing asecond electrical signal proportional to the term K6', where K is aproportionality constant which is a function of the time delay of themotor control unit, a second amplifier for developing a third electricalsignal whose polarity and magnitude are represented by the term G, asummation network having first and second input terminals coupled tosaid first and second amplifiers, respectively, said summation networkbeing responsive to said second and third electrical signals forproducing tan electrical output signal whose polarity changes each timethe load is driven to a point whereat continued energization of themotor in the same direction for the delay time of the motor control unitwould drive the load past a point whereat instantaneous reversal of themotor would drive the load to the predetermined position, and means forapplying said output signal to said selectively tactuable motor controlrneans, said selectively actuable means being responsive to said outputsignal for fully energizing said motor in one direction when said outputsignal is of one polarity, and for fully energizing said motor in theopposite direction in response to said output signal changing to theother polarity.

4. In a servo system wherein a displaceable load is movable, whendisplaced, toward a predetermined position of zero displacement and zerovelocity by an associated servomotor which is selectively fullyenergizable in either direction, a control unit for fully energizing themotor in a restoring direction to return the load to a point whereatfull energization of the motor in the reverse direction would return theload to the predetermined position, and for reversing the energizationof the motor after the point has been reached, said control unitcomprising: first means for generating a first electrical signalproportional to the term 0, where a represents the instantaneous loaddisplacement; second means including an amplifier coupled to said firstmeans and responsive to said first signal for producing a secondelectrical signal proportional to the term 6; third means including adifferentiating circuit and an amplifier circuit connected in cascade,said third means being coupled to said first means and being responsiveto said rst signal for developing a third electrical signal proportionalto the term K9', where represents the time rate of change of said tirstsignal and K represents a proportionality constant selected inaccordance with the time-delay characteristic of the servo system; asummation network including first and second input terminals coupled tosaid second and third means, respectively, said summation network beingresponsive to said second and third signals for combining said signalsto produce an electrical output signal corresponding to the algebraicsummation of said second and third signals; and selectively actuablemeans coupled between said summation network and the servomotor, saidselectively actuable means being responsive to said output signal forenergizing said servomotor in one direction when said output signal isof one polarity and for energizing said servo motor in the oppositedirection in response to said output signal changing to the oppositepolarity.

5. In a servo system wherein a displaceable load is movable, whendisplaced, toward a point of zero displacement and zero velocity by anassociated servomotor which is fully energizable in either directionunder the control of a selectively actuable motor control unit, a servocontrol circuit for actuating the motor control unit to fully energizethe motor in a restoring direction for returning the load to a pointwhereat full energization of the motor in the reverse direction wouldreturn the load to the point of zero displacement and zero velocity, andfor actuating the motor control unit thereafter to reverse theenergzation of the motor, said control circuit comprising: iirst meansfor generating a first electrical signal proportional to the term 9,where represents the instantaneous load displacement; second meansincluding an amplifier coupled to said irst means and responsive to saidfirst signal for producing a second electrical signal proportional tothe term 0; third means including a differentiating circuit and anelectronic amplier, said third means being coupled to said tirst meansand being responsive to said iirst signal for developing a thirdelectrical signal proportional to the term 0', where represents the timerate of change of said first signal; and a summation network coupled tosaid second and third means for combining said second and third signalsto produce an electrical output signal the polarity of which changeseach time the load has been driven to a point whereat continuedenergization of the servomotor in the same direction for the inherentdelay time of the motor control unit would dnve the load to a furtherpoint whereat full energization of the motor in the reverse directionwould return the load to a point of zero displacement and zero velocity,the motor control unit being responsive to the polarity of said outputsignal for controlling the direction of movement of the motor.

6. In a servo system wherein a displacement signal is generated eachtime a system load is displaced from a predetermined position, themagnitude and polarity of the displacement signal corresponding to themagnitude and displacement of the load, and wherein a reversible servomotor having a substantially constant acceleration-decelerationcharacteristic over the range of load displacement is operable formoving the load in a restoring direction under the control of aselectively actuable motor control unit, a servo control circuit forselectively actuating the motor control unit to fully energize the motorin a restoring direction for returning the load to a point whereat fullenergization of the motor in the reverse direction would return the loadto a point of zero displacement and zero velocity, and for reversing theenergization of thc motor thereafter, said control circuit comprising:first means including an amplifier responsive to the displacement signalfor producing a first electrical signal proportional to the term 0,where 6 represents the load displacement; second means including adifferentiating circuit and an electronic amplifier coupled in cascade,said second means being responsive to the displacement signal fordeveloping a second electrical signal proportional to the term fi, whererepresents the time rate of change of the displacement signal; and asummation network coupled to said tirst and second means and responsiveto said first and second signals for producing an electrical outputsignal the polarity of which changes each time the load has been drivento a point whereat continu-ed full energization of the motor in the samedirection for the delay time of the motor control unit would drive theload to the point whereat full energization of the motor in the reversedirection would return the load to a point of zero displacement and zerovelocity, the motor control unit being responsive to the polarity ofsaid output signal for controlling the direction of movement of themotor.

References Cited in the lile of this patent UNITED STATES PATENTS2,105,598 Hubbard Ian. 18, 1938 2,439,198 Bedford Apr. 6, 1948 2,446,567White et al Aug. l0, 1948 OTHER REFERENCES Electronic Instruments,Greenwood, Holdam and Macrae, McGraw-Hill Book Co., Inc., 1948, pp. 322and 327.

